BE.104 Spring
“Epidemiology: Test Development and Relative Risk”
J. L. Sherley
? Cause
Agent X
∆ Health
First, Some definitions
Morbidity =
sickness, disease, [toxicity] – Hard to quantify
Mortality =
death – Easy to quantify
Annual Death Rate =
Total deaths during specified 12 months
Number of persons in pop. @ middle of the period specified
Age-specific ADR = ADR for a specified age
Age-adjusted ADR = adjusted ADR (indexing for age differences, e.g., death
rates in nursing home versus general population)
Incidence = # of NEW cases in a population
during a specified period of time = “Rate of appearance in group at risk”
Number of persons exposed to risk
of developing disease in same
interval (by convention per 100,000 persons)
Prevalence = # of cases in population at a specified time
# of persons present in pop. at same time
(By convention per 100,000 persons)
= “Frequency”
[Prevalence α Incidence X duration of disease based on death or cure]
“Chronic disease will be more prevalent”
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Tests
disease
To determine these epi-parameters, we need to develop tests to detect and quantify
exposure
death
Develop tests
- Disease measurements (death is not all that easy to quantify
when you want death from a specific cause)
- Exposure measurements to X
- Measure X in the environment
Properties of a good test
Simple
Well tolerated < by all involved; subject & tester >
High throughout
Proven versus newly developed
Precise
Accurate: Sensitive, Specific, Predictive
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Categories of test results
w/D w/oD <Disease (D) Status
TP FP
Positive
Negative
<Test
FN TN
True positives,
False positives,
False negatives,
True negatives,
TP
FP
FN
TN
Sensitivity =
TP
x 100%;
TP + FN
(All the affected)
Ideally, = 100%
⇒ FN = 0
Sensitivity = the efficiency at detecting cases
Specificity =
TN
x 100%;
TN + FP
(All the unaffected)
Ideally = 100%
⇒ FP = 0
Specificity = efficiency at identifying non-cases
Predictive value (PV): the probability that individuals with a positive (negative) test have the disease
(are disease free). How accurate is the test value?
Positive PV =
TP/ (TP+FP) ; note: TP+FP = total positive tests. What fraction are true?
Negative PV =
TN/ (TN+FN); note: TN+TN = total negative tests. What fraction are true?
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Test quality depends on multiple factors
- Degree of difference between cases & controls for a given measure
- Set point for test threshold
Diabetes Example
Sensitivity & Specificity are co-variants with test threshold
In practice, set threshold based on:
1) Disease severity (i.e. don’t want to miss things that lead to death or severe injury)
2) Side-effects of response (i.e. don’t want to treat normals with potentially harmful treatment)
3) Must consider cost of unnecessary response
What is the point of this example?
Before designing a test to distinguish between affected and non-affected populations
we need to know the characteristics of the distribution of values of individuals in the two
compared populations.
First case of a “frequency plot” (= distribution).
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Risk
Much of modern epidemiology and environmental health science is concern with Risk
Risk- a measure of the likelihood that an event will occur in the future (usually adverse event; but
formally it could be positive or neutral)
Since there are no true seers or fortune-tellers, absolute measures of risk are hard to come by.
So, typically Risk is:
1) Past experience-based (“trial & error learning”)
What the risk of holding your hand for 1 minute in a candle flame
that you will burn your hand?
What about on a windy day? Etc.!
2) Seldom individual- population based
3) Often relative
A way to quantify the effect of a presumed risk factor or chemical agent
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Odds Ratio- An estimate of relative risk, RR
Consider a disease that occurs within two distinct populations; one known to be exposed to an agent,
the other known not to be exposed. How can we estimate the magnitude of any change in risk for
the disease that is associated with the exposure to the agent?
Number of Persons
Affected
Unaffected
Exposure
Yes
No
Total
If
a
a+c
Fraction of
affected
who were
exposed
a
c
a+c
b
d
b+d
is statistically different than
Total
a+b
c+d
a+b+c+d=N
b
b+d
Fraction of
unaffected
who were
exposed,
…then we can use the relative risk calculation to quantify the magnitude of the effect of
exposure to the agent on the occurrence of the disease.
Ideally:
100%
0%
Affected and unaffected
have equal likelihood of
exposure.
If these are equivalent,
then exposure is not an important
determinant of illness.
** Why are these seldom the ideal?
Genes, environment, luck, error
a = Number new cases who were exposed during period of investigation = Incidenceexposed
a+b
Total number exposed during same period (i.e. at risk)
c = Number new cases who were unexposed during period of investigation = Incidenceunexposed
c+d
Total number of unexposed during same period
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"Odds Ratio" ≈
Iexposed
Iunexposed
= a (c + d) = Relative Risk
(a +b ) c
=
ac + ad
ac + bc
≈
ad
bc
when a + c
<<<
b+d
total
total
affected
unaffected
which is often the case!!!
[Statistical Test: often chi-square for case of RR = 1.0; w/ 95% CI for chi-square distribution]
What level of RR is meaningful?
Given that the calculation is statistically signficant, how can you increase your
level of confidence that an estimate of RR is meaningful in terms of public health?
1) Magnitude: consider 1.2 vs 20
Comfort zone @ RR ≥ 5.0
2) Dose response analysis
Although seeing a dose-response for a suspected toxic factor and relative risk increases
confidence for significance of small RR and cause-effect relationship, it is hard to do
experimentally because of ethics, unless by reducing exposure.
What else could be done to evaluate dose-response?
Stratification- the “dose response” of epidemics & environmental health scientists
Stratify RR analyses by e.g.,: Place-
up vs down stream & distance
up vs down wind & distance
outdoors vs indoor
Personsworkers vs non-workers
fish eaters vs others
children vs adults
Timebefore vs after the plant
resident vs moved away
new resident vs old resident
Look for statistically significant associations with RR
One major limitation: Decrease sample size for group stratification (More later on this!)
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Decreased power to detect RR ≠ 1.0
Can RR < 1.0?
Yes when exposure to an agent reduces the incidence of the illness
E.g., in successful drug trials
Public Policy Reponses to RR estimates are tempered by another consideration.
Given that a factor greatly increases the risk for a disease, how many in the population
have that factor?
How much of the disease burden in the population can be attributed to that factor?
Attributable Risk, AR in the population =
p(r-1)
p(r-1) + 1
where r = RR, p = proportion of the population with the risk factor (i.e., exposure)
AR tells us that a relative risk of 2 could be very significant if a large fraction of the population
has that risk factor
Cancer rates and drinking water, air quality. How much of total cancer burden
is due to factors of small RR that effect large populations?
Similarly- diet and heart disease
In contrast-
If few people smoked, the RR 10-20 for cigarette smoking would still contribute
a lot to overall lung cancer rates. As it is, if smoking prevalence were even
10%, then 50% of the lung cancers would be attributed to smoking.
A final consideration for RR:
What do you know if I tell you that the left half of the class has a RR = 106 for receiving a billion $
today compared to the right half of the class? That the left half of the room is associated with
greater likelihood of getting money. What do you need to know to evaluate this information?
What do you need to know before you quit school?
What if the right half’s “absolute risk" is 10-12?
What if it is 10-2?
We really need to have a measure of absolute risk. More to come on this.
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